never had that happen, but I can only assume a strip that is sealed from front to back of the garage, as long as the pad overall flows downwards towards the door, will help to lead the melt out the garage door. If It lingers on the sides of the pad, and drips between the pad and the foundation, it can cause erosion of the earth underneath and that can lead to massive settling. Was this a recent pour? Or was it this way when you moved in?

Sometimes you can call the "Mud Jack" people, they can prop up the sides and direct the flow to the middle. You might have settling already since it moves to the side. I have seen the issue with my neighbors in Westminster since they hosed out their garage seasonally, and that caused erosion. The Mud Jack process helped get things back to the proper grade.

I have a similar issue. Water tends to spread out a little too much to the sides of my garage than I like. I was thinking of getting some cheap caulk and running a bead along the floor to channel water back towards the door.

It wouldn't be permanent - I'm sure my kids would destroy the line quickly, but it would at least be an interesting experiment.